Calculating Heights on the Ferris Wheel

[urthatarget]

In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 50 seconds, then

h(t) = 125sin (pi/25t - pi/2) + 125

represents the height (h), in feet, of a seat on the wheel as a function of time (t), where t is measured in seconds. The ride begins when t = 0.


a.) During the first 50 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 125 feet above the ground?

b.) During the first 100 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 250 feet above the ground?

c.) During the first 50 seconds of the ride, over what interval of time (t) is an individual on the Ferris Wheel more than 125 feet above the ground?

Can someone help me solve part A so I can do the rest by myself. Thank you very much!

 

[rock.freak667]

a.) During the first 50 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 125 feet above the ground?

They are simply saying, during one revolution, when is h(t) = 125. Solve for t.

 

[HallsofIvy]

In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 50 seconds, then

h(t) = 125sin (pi/25t - pi/2) + 125

You mean h(t)= 125 sin((pi/25)t- pi/2)+ 125

represents the height (h), in feet, of a seat on the wheel as a function of time (t), where t is measured in seconds. The ride begins when t = 0.


a.) During the first 50 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 125 feet above the ground?

Solve the equation h(t)= 125 sin((pi/25)t- pi/2)+ 125= 125. For what values of x is sin(x)= 0?

b.) During the first 100 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 250 feet above the ground?

c.) During the first 50 seconds of the ride, over what interval of time (t) is an individual on the Ferris Wheel more than 125 feet above the ground?

Can someone help me solve part A so I can do the rest by myself. Thank you very much!